Copyright 2024
Hardback
ISBN 9780367321789
208 Pages 17 Color & 36 B/W Illustrations
July 7, 2023 by CRC Press
Deep learning is an important element of artificial intelligence, especially in applications such as image classification in which various architectures of neural network, e.g., convolutional neural networks, have yielded reliable results. This book introduces deep learning for time series analysis, particularly for cyclic time series. It elaborates on the methods employed for time series analysis at the deep level of their architectures. Cyclic time series usually have special traits that can be employed for better classification performance. These are addressed in the book. Processing cyclic time series is also covered herein.
An important factor in classifying stochastic time series is the structural risk associated with the architecture of classification methods. The book addresses and formulates structural risk, and the learning capacity defined for a classification method. These formulations and the mathematical derivations will help the researchers in understanding the methods and even express their methodologies in an objective mathematical way. The book has been designed as a self-learning textbook for the readers with different backgrounds and understanding levels of machine learning, including students, engineers, researchers, and scientists of this domain. The numerous informative illustrations presented by the book will lead the readers to a deep level of understanding about the deep learning methods for time series analysis.
PREFACE. I-FUNDAMENTALS OF LEARNING. Introduction to Learning. Learning Theory. Pre-processing and Visualisation. II ESSENTIALS OF TIME SERIES ANALYSIS. Basics of Time Series. Multi-Layer Perceptron (MLP) Neural Networks for Time Series Classification. Dynamic Models for Sequential Data Analysis. III DEEP LEARNING APPROACHES TO TIME SERIES CLASSIFICATION. Clustering for Learning at Deep Level. Deep Time Growing Neural Network. Deep Learning of Cyclic Time Series. Hybrid Method for Cyclic Time Series. Recurrent Neural Networks (RNN). Convolutional Neural Networks. Bibliography.
Copyright 2023
Hardback
ISBN 9780367900427
288 Pages
July 11, 2023 by Chapman & Hall
Four-Dimensional Manifolds and Projective Structure may be considered ?rst as an introduction to di?erential geometry and, in particular, to 4?dimensional manifolds, and secondly as an introduction to the study of projective structure and projective relatedness in manifolds.
The initial chapters mainly cover the elementary aspects of set theory, linear algebra, topology, Euclidean geometry, manifold theory and differential geometry, including the idea of a metric and a connection on a manifold and the concept of curvature. After this, the author dives deeper into 4-dimensional manifolds and, in particular, the positive definite case for the metric. The book also covers Lorentz signature and neutral signature in detail and introduces, and makes use of, the holonomy group of such a manifold for connections associated with metrics of each of these three possible signatures. A brief interlude on some key aspects of geometrical symmetry precedes a detailed description of projective relatedness, that is, the relationship between two symmetric connections (and between their associated metrics) which give rise to the same geodesic paths.
Offers a detailed, straightforward discussion of the basic properties of (4-dimensional) manifolds.
Introduces holonomy theory, and makes use of it, in a novel manner.
Suitable for postgraduates and researchers, including masterfs and PhD students.
1. Algebra, Topology and Geometry. 1.1. Notation. 1.2. Groups. 1.3. Vector Spaces and Linear Transformations. 1.4. Dual Spaces and Bilinear Forms. 1.5. Eigen-structure, Jordan Canonical Forms and Segre Types. 1.6. Lie algebras. 1.7. Topology. 1.8. Euclidean Geometry. 2. Manifold Theory. 2.1. Manifolds. 2.2. The Manifold Topology. 2.3. Vectors, Tensors and their Associated Bundles. 2.4. Vector and Tensor Fields. 2.5. Derived Maps and Pullbacks. 2.6. Integral Curves of Vector Fields. 2.7. Submanifolds and Quotient Manifolds. 2.8. Distributions. 2.9. Linear Connections and Curvature. 2.10. Lie Groups and Lie Algebras. 2.11. The Exponential Map for G. 2.12. Covering Manifolds. 2.13. Holonomy Theory. 3. Four-Dimensional Manifolds. 3.1. Metrics on 4-dimensional Manifolds. 3.2. The Connection, the Curvature and Associated Tensors. 3.3. Algebraic Remarks, Bivectors and Duals. 3.4. The Positive Definite Case and Tensor Classification. 3.5. The Curvature and Weyl Conformal Tensor. 3.6. The Lie Algebra o(4). 3.7. The holonomy structure of (M,g). 3.8. Curvature and Metric. 3.9. Sectional Curvature. 3.10. The Ricci Flat Case. 4. Four-Dimensional Lorentz Manifolds. 4.1. Lorentz Tangent Space Geometry. 4.2. Classification of Second Order Tensors. 4.3. Bivectors in Lorentz Signature. 4.4. The Lorentz Algebra o(1,3) and Lorentz Group. 4.5. The Curvature and Weyl Conformal Tensors. 4.6. Curvature Structure. 4.7. Sectional Curvature. 4.8. The Ricci Flat (Vacuum) Case. 5. Four-Dimensional Manifolds of Neutral Signature. 5.1. Neutral Tangent Space Geometry. 5.2. Algebra and Geometry of Bivectors. 5.3. Classification of Symmetric Second Order Tensors. 5.4. Classification of Bivectors. 5.5. The Lie Algebra o(2,2). 5.6. The Curvature Tensor. 5.7. The Weyl Conformal Tensor I. 5.8. The Weyl Conformal Tensor II. 5.9. Curvature Structure. 5.10. Sectional Curvature. 5.11. The Ricci-Flat Case. 5.12. Algebraic Classification Revisited. 6. A Brief Discussion of Geometrical Symmetry. 6.1. Introduction. 6.2. The Lie Derivative. 6.3. Symmetries of the Metric Tensor. 6.4. Affine and Projective Symmetry. 6.5. Orbits and isotropy algebras for K(M). 7. Projective Relatedness. 7.1. Recurrence and Holonomy. 7.2. Projective Relatedness. 7.3. The Sinjukov Transformation. 7.4. Introduction of the Curvature Tensor. 7.5. Einstein Spaces. 7.6. Projective Relatedness and Geometrical Symmetry. 7.7. The 1?form Õ. 7.8. Projective Relatedness in 4-dimensional Manifolds.
@
Multi-Pack Set
ISBN 9780367208363
768 Pages 8 B/W Illustrations
July 3, 2023 by Chapman & Hall
Model theory is the meta-mathematical study of the concept of mathematical truth. After Afred Tarski coined the term Theory of Models in the early 1950fs, it rapidly became one of the central most active branches of mathematical logic. In the last few decades, ideas that originated within model theory have provided powerful tools to solve problems in a variety of areas of classical mathematics, including algebra, combinatorics, geometry, number theory, and Banach space theory and operator theory.
The two volumes of Beyond First Order Model Theory present the reader with a fairly comprehensive vista, rich in width and depth, of some of the most active areas of contemporary research in model theory beyond the realm of the classical first-order viewpoint. Each chapter is intended to serve both as an introduction to a current direction in model theory and as a presentation of results that are not available elsewhere. All the articles are written so that they can be studied independently of one another.
The first volume is an introduction to current trends in model theory, and contains a collection of articles authored by top researchers in the field. It is intended as a reference for students as well as senior researchers.
This second volume contains introductions to real-valued logic and applications, abstract elementary classes and applications, interconnections between model theory and function spaces, nonstucture theory, and model theory of second-order logic.
A coherent introduction to current trends in model theory.
Contains articles by some of the most influential logicians of the last hundred years. No other publication brings these distinguished authors together.
Suitable as a reference for advanced undergraduate, postgraduates, and researchers.
Material presented in the book (e.g, abstract elementary classes, first-order logics with dependent sorts, and applications of infinitary logics in set theory) is not easily accessible in the current literature.
The various chapters in the book can be studied independently.
Table of Contents of Volume I
I. Model Theory of Strong Logics. 1. Expressive Power of Infinitary [0, 1]-logics. 2. Scott Processes. 3. Failure of 0-1 Law for Sparse Random Graph in Strong Logics. II. Model Theory of Special Classes of Structures. 4. Maximality of Continuous Logic. 5. Model Theory and Metric Convergence I: Metastability and dominated convergence. 6. Randomizations of Scattered Sentences. 7 Existentially Closed Locally Finite Groups. 8. Analytic Zariski Structures and Non-Elementary Categoricity. III. Abstract Elementary Classes. 9. Hanf Numbers and Presentation Theorems in AECs. 10. A Survey on Tame Abstract Elementary Classes.
Table of Contents of Volume II
I. Real-Valued Structures and Applications. 1. Metastable Convergence and Logical Compactness. 2. Model Theory for Real-Valued Structures. 3. Spectral Gap and Definability. II. Abstract Elementary Classes and Applications. 4. Lf groups, AEC amalgamation, few automorphisms. III. Model Theory and Topology of Spaces of Functions. 5. Cp-Theory for Model Theorists. IV. Constructing Many Models. 6. General Non-Structure Theory. V. Model Theory of Second Order Logic. 7. Model Theory of Second Order Logic.
Volume 92 in the series De Gruyter Studies in Mathematics
The study of minimal surfaces is an important subject in differential geometry, and Nevanlinna theory is a classical subject in complex analysis. This book discusses the interaction between these two subjects. In particular, it describes the study of the value distribution properties of the Gauss map of minimal surfaces through Nevanlinna theory, a project initiated by the prominent differential geometers Shiing-Shen Chern and Robert Osserman.
Presents the basis theory of minimal surfaces.
Develops the classical theory of holomorphic curves in the projective space with Ahlfors' approach
Examines the y the value distribution properties for the Gauss maps of the immersed harmonic surfaces.
Author information
Min Ru, University of Houston, U.S.A.
Analysis
Applied Mathematics
Mathematics
In the series De Gruyter Textbook
Mathematical Logic: An Introduction is a textbook that uses mathematical tools to
investigate mathematics itself. In particular, the concepts of proof and truth are examined.
The book presents the fundamental topics in mathematical logic and presents clear and
complete proofs throughout the text. Such proofs are used to develop the language of
propositional logic and the language of first-order logic, including the notion of a formal
deduction. The text also covers Tarskifs definition of truth and the computability concept.
It also provides coherent proofs of Godelfs completeness and incompleteness theorems.
Moreover, the text was written with the student in mind and thus, it provides an accessible
introduction to mathematical logic. In particular, the text explicitly shows the reader
how to prove the basic theorems and presents detailed proofs throughout the book. Most
undergraduate books on mathematical logic are written for a reader who is well-versed
in logical notation and mathematical proof. This textbook is written to attract a wider
audience, including students who are not yet experts in the art of mathematical proof.
This text written with the student in mind provides an accessible introduction to logic,
explicitly showing the reader how to produce and compose the proofs of the basic theorems
in mathematical logic through numerous examples and exercises.
Daniel W. Cunningham is a Professor Emeritus of Mathematics at SUNY Buffalo State, a
campus of the State University of New York. Daniel received a Ph.D. in Mathematics from
UCLA, specializing in mathematical logic. He currently teaches at California State University
at Fresno. Cunninghamfs research focus is in set theory, and has recently published
two research papers and two textbooks
Algebra and Number Theory
Logic
Logic and Set Theory
Mathematics
Philosophy
Part of the multi-volume work Non-Invertible Dynamical Systems
Volume 69/3 in the series De Gruyter Expositions in Mathematics
This Volume 3, is part of a series entitled Non-Invertible Dynamical Systems and presents topological dynamics, thermodynamic formalism, and fractal geometry of rational functions of the Riemann sphere.Volume 1 covers topological pressure, entropy, variational principle, equilibrium states and abstract ergodic theory. Volume 2 presents distance expanding maps, Lasota-Yorke maps and fractal geometry with applications to conformal IFSs
This Volume 3, is part of a series entitled Non-Invertible Dynamical Systems and presents topological dynamics, thermodynamic formalism, and fractal geometry of rational functions of the Riemann sphere.
Mariusz Urba?ski, University of North Texas, USA; Mario Roy, York University, Canada; Sara Mundy, John Cabot University, Italy.
Analysis
Differential Equations and Dynamical Systems
Geometry and Topology
Mathematics
Probability and Statistics